Holt Algebra Variables and Expressions 1-1 Variables and Expressions Holt Algebra 1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation

Holt Algebra Variables and Expressions Warm Up Add or subtract (9) – 8 4. Multiply or divide ÷ (10) ÷

Holt Algebra Variables and Expressions Translate between words and algebra. Evaluate algebraic expressions. Objectives

Holt Algebra Variables and Expressions variable constant numerical expression algebraic expression evaluate Vocabulary

Holt Algebra Variables and Expressions A variable is a letter or a symbol used to represent a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic expression may contain variables, constants, and operations.

Holt Algebra Variables and Expressions You will need to translate between algebraic expressions and words to be successful in math. Plus, sum, increased by + –  Minus, difference, less than Times, product, equal groups of Divided by, quotient

Holt Algebra Variables and Expressions These expressions all mean “2 times y”: 2y 2(y) 2y (2)(y) 2 x y (2)y Writing Math

Holt Algebra Variables and Expressions Give two ways to write each algebra expression in words. A. 9 + r B. q – 3 the sum of 9 and r 9 increased by r the product of m and 7 m times 7 the difference of q and 3 3 less than q the quotient of j and 6 j divided by 6 Example 1: Translating from Algebra to Words C. 7m D. j  6

Holt Algebra Variables and Expressions 1a. 4 - n 1b. 1c. 9 + q 1d. 3(h) 4 decreased by n the sum of 9 and q the quotient of t and 5 the product of 3 and h Give two ways to write each algebra expression in words. Check It Out! Example 1 n less than 4 t divided by 5 q added to 9 3 times h

Holt Algebra Variables and Expressions To translate words into algebraic expressions, look for words that indicate the action that is taking place. Put together, combine Add Subtract MultiplyDivide Find how much more or less Put together equal groups Separate into equal groups

Holt Algebra Variables and Expressions John types 62 words per minute. Write an expression for the number of words he types in m minutes. m represents the number of minutes that John types. 62 · m or 62m Think: m groups of 62 words Example 2A: Translating from Words to Algebra

Holt Algebra Variables and Expressions Roberto is 4 years older than Emily, who is y years old. Write an expression for Roberto’s age y represents Emily’s age. y + 4 Think: “older than” means “greater than.” Example 2B: Translating from Words to Algebra

Holt Algebra Variables and Expressions Joey earns $5 for each car he washes. Write an expression for the number of cars Joey must wash to earn d dollars. d represents the total amount that Joey will earn. Think: How many groups of $5 are in d? Example 2C: Translating from Words to Algebra

Holt Algebra Variables and Expressions Use the Commutative, Associative, and Distributive Properties to simplify expressions. Combine like terms. Objectives

Holt Algebra Variables and Expressions The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. 4x – 3x + 2 Like terms Constant

Holt Algebra Variables and Expressions A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1. 1x 2 + 3x Coefficients

Holt Algebra Variables and Expressions

Holt Algebra Variables and Expressions The Distributive Property is used with Addition to Simplify Expressions. The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

Holt Algebra Variables and Expressions Example 2A: Using the Distributive Property with Mental Math Write the product using the Distributive Property. Then simplify. 5(59) 5(50 + 9) 5(50) + 5(9) Rewrite 59 as Use the Distributive Property. Multiply. Add.

Holt Algebra Variables and Expressions 8(33) 8(30 + 3) 8(30) + 8(3) Rewrite 33 as Use the Distributive Property. Multiply. Add. Example 2B: Using the Distributive Property with Mental Math Write the product using the Distributive Property. Then simplify.

Holt Algebra Variables and Expressions Check It Out! Example 3 Simplify by combining like terms. 3a. 16p + 84p 16p + 84p 100p 16p + 84p are like terms. Add the coefficients. 3b. –20t – 8.5t 2 –20t – 8.5t 2 20t and 8.5t 2 are not like terms. –20t – 8.5t 2 Do not combine the terms. 3m 2 + m 3 3m 2 and m 3 are not like terms. 3c. 3m 2 + m 3 Do not combine the terms. 3m 2 + m 3

Holt Algebra Variables and Expressions Example 4: Simplifying Algebraic Expressions Simplify 14x + 4(2 + x). Justify each step. 14x + 4(2) + 4(x)Distributive Property Multiply. Commutative Property Associative Property Combine like terms. 14x x (14x + 4x) x + 4x x x + 4(2 + x) Procedure Justification

Holt Algebra Variables and Expressions 6(x) – 6(4) + 9 Distributive Property Multiply. Combine like terms. 6x – x – 15 6(x – 4) Procedure Justification Check It Out! Example 4a Simplify 6(x – 4) + 9. Justify each step.

Holt Algebra Variables and Expressions – 12x – 5x + x + 3a Commutative Property Combine like terms. –16x + 3a – 12x – 5x + 3a + x Procedure Justification Check It Out! Example 4b Simplify −12x – 5x + 3a + x. Justify each step.

Holt Algebra Variables and Expressions Lesson Quiz: Part I Simplify each expression Write each product using the Distributive Property. Then simplify. 3. 5($1.99) 4. 6(13) ($2) – 5($0.01) = $9.95 6(10) + 6(3) = 78

Holt Algebra Variables and Expressions Lesson Quiz: Part II Simplify each expression by combining like terms. Justify each step with an operation or property x – x 8. 24a + b 2 + 3a + 2b x 27a + 3b c 2 – 9c 14c 2 – 9c

Holt Algebra Variables and Expressions Lou drives at 65 mi/h. Write an expression for the number of miles that Lou drives in t hours. Check It Out! Example 2a t represents the number of hours that Lou drives. 65tThink: number of hours times rate per hour.

Holt Algebra Variables and Expressions Miriam is 5 cm taller than her sister, than her sister who is m centimeters tall. Write an expression for Miriam’s height in centimeters. Check It Out! Example 2b m represents Miriam’s sister's height in centimeters. m + 5Think: Miriam's height is 5 added to her sister's height.

Holt Algebra Variables and Expressions Check It Out! Example 2c d represents the amount of money Elaine will earn each day. 32dThink: The number of days times the amount Elaine would earn each day. Elaine earns $32 per day. Write an expression for the amount she earns in d days.

Holt Algebra Variables and Expressions To evaluate an expression is to find its value. To evaluate an algebraic expression, substitute numbers for the variables in the expression and then simplify the expression.

Holt Algebra Variables and Expressions Evaluate each expression for a = 4, b =7, and c = 2. A. b – c b – c = 7 – 2 Substitute 7 for b and 2 for c. = 5 B. ac ac = 4 ·2 = 8 Substitute 4 for a and 2 for c. Simplify. Example 3: Evaluating Algebraic Expression

Holt Algebra Variables and Expressions Evaluate each expression for m = 3, n = 2, and p = 9. a. mn b. p – n c. p ÷ m Check It Out! Example 3 mn = 3 · 2 p – n = 9 – 2 = 7 = 6 p ÷ m = 9 ÷ 3 = 3 Substitute 3 for m and 2 for n. Simplify. Substitute 9 for p and 2 for n. Simplify. Substitute 9 for p and 3 for m. Simplify.

Holt Algebra Variables and Expressions Example 4a: Recycling Application Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. Write an expression for the number of bottles needed to make s sleeping bags. The expression 85s models the number of bottles to make s sleeping bags.

Holt Algebra Variables and Expressions Find the number of bottles needed to make 20, 50, and 325 sleeping bags. Evaluate 85s for s = 20, 50, and 325. s85s (20) = (50) = (325) = 27,625 Example 4b: Recycling Application Continued Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. To make 20 sleeping bags 1700 bottles are needed. To make 50 sleeping bags 4250 bottles are needed. To make 325 sleeping bags 27,625 bottles are needed.

Holt Algebra Variables and Expressions A replacement set is a set of numbers that can be substituted for a variable. The replacement set in Example 4 is (20, 50, and 325). Writing Math

Holt Algebra Variables and Expressions To make one sweater, 63 twenty ounce plastic drink bottles must be recycled. Write an expression for the number of bottles needed to make s sweaters. The expression 63s models the number of bottles to make s sweaters. Check It Out! Example 4a

Holt Algebra Variables and Expressions Find the number of bottles needed to make 12, 25 and 50 sweaters. Evaluate 63s for s = 12, 25, and 50. s63s (12) = (25) = (50) = 3150 To make 12 sweaters 756 bottles are needed. To make 25 sweaters 1575 bottles are needed. To make 50 sweaters 3150 bottles are needed. Check It Out! Example 4b Continued To make one sweater, 63 twenty ounce plastic drink bottles must be recycled.

Holt Algebra Variables and Expressions Give two ways to write each algebraic expression in words. 1. j – p 3. Mark is 5 years older than Juan, who is y years old. Write an expression for Mark’s age. The difference of j and 3; 3 less than j. 4 times p; The product of 4 and p. y + 5 Lesson Quiz: Part I

Holt Algebra Variables and Expressions Evaluate each expression for c = 6, d = 5, and e = c + d Shemika practices basketball for 2 hours each day. d e d2d 10 hours; 24 hours; 40 hours Lesson Quiz: Part II 6. Write an expression for the number of hours she practices in d days. 7. Find the number of hours she practices in 5, 12, and 20 days.